Delta rays were named well before the neutron.......
Enrico Fermi suggested that the imbalance in beta decay energy was carried off by a massless particle which he suggested might be called a neutron. As the particle was never detected and some scientists thought he was grabbing at straws, the name really did not make the literature to any extent.
When Chadwick discovered the neutron, a few years later, he named this real, demonstrable particle "neutron". Alpha, Beta, Gamma, Delta were already taken. As the near proton mass particle predicted years earlier by Rutherford, was charge neutral, neutron became its name. It is unknown if Chadwick was aware of Fermi's "neutron"....Regardless, the neutral neutron was real, massive and easily demonstrable.
Alpha, Beta, Gamma and Delta were all named from the study of naturally radioactive elements early on, (1890's through the first decade of the twentieth century). Common, natural radioactive elements of that early time did not emit detectable neutrons. Early instruments could not detect them. Neutrons had to be ripped from a nucleus via fission or fusion. The old Greek alphabet had fallen by the wayside by the 1930's as radiation physics had gone beyond the stunned amazement of the early pioneers plowing new strange ground, naming mysterious particles based on the Greek.
However, in the late 40's and early 50's with a massive new rash of mesons being discovered daily, it seemed, the Greek alphabet was once again hauled out of retirement.... and then the fun began!! The particle zoo never stopped getting new little radiative, short lived, "animalcules", not abating to this day!
We now know that natural U238 self-fissions emitting neutrons at an incredibly low rate. No one in the early years knew anything about the neutron prior to Chadwick's discovery and fission was still 4 years beyond the discovery of the neutron. In 1934, Ida Noddack, a German chemist and physicist, predicted the possibility of fission, (liquid water drop model). Little note was made of it. It was Lise Meitner and her nephew, Otto Frisch, who remembered Noddack's paper and explained the mystery to Otto Hann of what his experimental results really meant. Hann was mystified and at a loss to explain, so he enlisted Lise's help. (Hann had once worked with her and valued her physics knowledge.) While out skiing with her physicist nephew, they sat on a log to rest in the snow, discussed the matter, and figured it out.
The discovery of the neutron changed nuclear physics, solving many issues within the field and opening up a new vista that expanded nuclear physics at near light speed.
Fermi, casting about for a new name, called his mysterious vapor particle, the "neutrino", (little neutral one -Italian). Finally, in the mid-fifties, shortly after Fermi died, claims were made of the discovery of his neutrino.
Note: The neutrino became a more of less accepted concept, in spite of its not being discovered. This happened in the late 30's and early 40's as it allowed physicists to explain beta decay of the neutron within the nucleus in a way that made sense.